Characterization of the Mixed-Phase States Using Self-Similarity Phenomenon for First-Order Magnetocaloric Metamagnets

Abstract

The understanding of how magnetocaloric metamagnets transition near the metamagnetic transition region is profoundly important to fundamental research and the application of near-room temperature magnetic refrigeration. Metamagnetic transition is characterized by field-induced transitions between the ferromagnetic (FM) and the paramagnetic (PM) state at temperatures above the Curie temperature. The metamagnetic region has been experimentally shown to exhibit coexistence of FM and PM phases attributed to the materials' intrinsically layered crystallographic structures. An analytical characterization approach is proposed to numerically calculate the fractional compositions of the mixed-state phases. The fractional composition state functions for magnetocaloric metamagnets are formulated by utilizing the self-similarity phenomenon within the material's (∂ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> /∂ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> curves. This self-similarity is demonstrated by the collapse of the (∂ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> /∂ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> curves at different field values onto a single scaled curve with low index of dispersion. To study the effectiveness of this new analytical approach, the fractional compositions functions for Gd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> was evaluated. The calculated Gd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> fractional composition state functions demonstrate considerable characteristic agreements with previous experimental results. Knowledge of the FM and PM cluster compositions near the metamagnetic region impacts the calculation of Maxwell's Relation and provides a new numerical perspective for enhancing the magnetocaloric properties via the methods of nano-engineering or chemical substitution processes.